Personal relationship with God
The assertion that "Christianity is a relationship" is, at its most basic, a part of an apologetic or evangelistic technique. When talking to people who think that religion is a bad thing, the Christian attempts to convince the listener that Christianity is not like other religions, in fact, it's so different that it's not really a religion at all (one can presume that we were saved from claims that Christianity is "religion 2.0" by the fact that there was no Internet when people were thinking this stuff up). It's the religious equivalent of the spammer's claim that spam is that which we don't do. robhu ran into this sort of claim recently. Not all Christians go along with this sort of word-game: hurrah for woodpijn, who is happy to admit that Christianity is in fact a religion.
It's more interesting to hear people talking of a "personal relationship with God". I think it means that the Christian relates to God in prayer a bit like they'd relate to humans by talking and listening (God being a person with whom such a relationship is possible, albeit a vastly superior sort of person). This gets you into trouble straight away. If, for example, all the people who claim have they such a relationship really did, they would all agree with each other because when the question of what God thought about something arose, they could just ask him. I've mentioned this in the past, but the most recent thread was started off when the Christians on uk.r.c told an atheist that he'd misunderstood Christianity by taking it as a set of beliefs, because in fact (you guessed it) "it's a relationship with God". I made my usual point that God doesn't seem to have his story straight when talking to different people. A couple of posters responded that this was a simplistic view of a relationship, and that the things about which Christians disagree on uk.r.c weren't very important to God. You can see my response to that.
Mark Goodge responded differently, by saying that he'd meant "relationship" in the sense that someone just is someone else's son or daughter, regardless of how often they actually speak. Christians are God's adopted children, even if they believe wildly different things.
As I said in my reply, I can see his point (after all, I thought liberals Christians were real Christians when I was an evangelical). But I wonder how that theology works: who is adopted, and how? Is everyone who claims to be a Christian adopted, including the extreme liberals, the Mormons, and so on? It'll be interesting to see what Mark's argument is here.
All the responses still leave the question of just how important believing stuff is to God, in the view of these Christians. The Christian church likes to have schisms on the very issues that the uk.r.christians spend a lot of time debating, so it seems these issues are pretty serious. I've certainly run into Christians who thought you cannot be an actively gay Christian, a Catholic Christian, a Christian who doesn't believe that Jesus was God, or a Christian who doesn't believe that God exists at all. If these things really are important to God, though, you'd have thought he'd tell his children his views. We must conclude that what God considers important is the stuff that everyone who is a Christian agrees on, namely that you should be nice to people, that Jesus was probably a good bloke, and that it's important to gather with your friends every so often and sing songs (although not with musical accompaniment, obviously: Christians must be like popular 80s beat combo The Flying Pickets). On this basis, I think I could be a Christian after all.